Cooling of an electric synchronous motor is known, such as in US20050012409 that has a large number of current-carrying wire windings arranged in corresponding recesses of a stator, where a longitudinal cooling conduit, impinged on by a cooling liquid, is introduced into each of the recesses. The cooling conduits provided between the wire windings and an air gap of the synchronous motor hereby form a heat shield to protect the rotor, which is made of a permanently magnetized material. The cooling conduits, formed as separate metal tubes, require not only additional installation space, but permit only a limited cooling of the adjacent wire windings as a result of the comparatively high thermal contact resistance.